上海交通大学学报

上海交通大学学报 ›› 2023, Vol. 57 ›› Issue (2): 177-182.doi: 10.16183/j.cnki.jsjtu.2021.337

所属专题： 《上海交通大学学报》2023年“船舶海洋与建筑工程”专题

• 船舶海洋与建筑工程 • 上一篇    下一篇

双层Boussinesq水波方程速度公式的修正

刘忠波1(), 韩青亮1, 任双双1, 王彦1, 房克照2   

  1. 1.大连海事大学 交通运输工程学院, 辽宁 大连 116026
    2.大连理工大学 海岸和近海工程国家重点实验室, 辽宁 大连 116024
  • 收稿日期:2021-09-06 修回日期:2021-12-10 接受日期:2021-12-16 出版日期:2023-02-28 发布日期:2023-03-01
  • 作者简介:刘忠波(1976-),副教授,博士生导师,现主要从事波浪水动力研究; E-mail: liuzhongbo@dlmu.edu.cn.
  • 基金资助:
    国家自然科学基金(52171247);国家自然科学基金(51779022);国家自然科学基金(52071057)

Modification of Velocity Formulations in a Two-Layer Boussinesq-Type Model for Water Waves

LIU Zhongbo1(), HAN Qingliang1, REN Shuangshuang1, WANG Yan1, FANG Kezhao2   

  1. 1. College of Transportation Engineering, Dalian Maritime University, Dalian 116026, Liaoning, China
    2. State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, Liaoning, China
  • Received:2021-09-06 Revised:2021-12-10 Accepted:2021-12-16 Online:2023-02-28 Published:2023-03-01

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摘要：

为提高Boussinesq水波方程中的速度精度,以最高空间导数为2的双层Boussinesq方程为研究对象,提出增加带有常系数的三阶项以修正速度公式.适用水深在0<kh<8(k为波数,h为静水深)范围内,以方程的水平速度和垂向速度与Stokes线性波速度解析解的积分误差最小为目标,优化系数取值.在1%误差内,改进公式水平速度和垂向速度的适用水深kh分别为7.34和7.83,均比原计算公式适用范围大.利用数值模型对稳态波和聚焦波演化进行计算,将最大波峰下的水平速度分别与流函数解析解和试验结果进行对比,发现改进后的吻合程度更高,验证了改进公式的有效性.研究表明,改进公式的速度精度有较大幅度提高,该方法可为其他Boussinesq模型的速度场改进提供重要参考.

关键词: Boussinesq水波方程, 速度公式, 解析解, 数值模拟

Abstract:

In order to improve the accuracy of velocity formulation in a Boussinesq-type wave model, with a two-layer Boussinesq-type model with the highest spatial derivative of 2 being chosen as the research object, a third-order term with constant coefficient is proposed to modify the velocity formulation. The coefficient is optimized by minimizing the error between the summation of the integration of horizontal and vertical velocities of the equation and that of the analytical linear Stokes wave velocity components in the range of 0<kh< 8 (where k is wave number, h is still water depth). At a 1% tolerance error, the applicable water depths of the modified formulations for horizontal and vertical velocities are up to kh=7.34 and kh=7.83, respectively, which are larger than those of the original formulations. The evolution of the steady-state wave and the focused wave is numerically simulated by using the numerical model. The horizontal velocity under the maximum surface elevation crest is in good agreements with the analytical solution of stream function and published experimental data, which verifies the effectiveness of the modified formulations. The studies show that the velocity accuracy of the improved equation is greatly improved. This method provides an important reference for the improvement of velocity field of other Boussinesq-type models.

Key words: Boussinesq-type equation, velocity formulation, analytical solution, numerical simulation

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